Example 1.5:  Isobutylene decomposed to its products and the following data were obtained. 

 

 

CA/(mol/L)

 

1.00

 

0.943

 

0.892

 

0.805

 

0.733

 

0.579

 

0.407

 

-rA/ (mol/(L·s))

 

2.02 ´ 10-4

 

1.80 ´ 10-4

 

1.61 ´ 10-4

 

1.31 ´ 10-4

 

1.09 ´ 10-4

 

6.77 ´ 10-5

 

3.35 ´ 10-5

 

Estimate the overall order of reaction.

 

Solution:  For a chemical reaction that is nth order, a plot of ln(-rA) versus ln(CA) yields a straight line (Equation 1.25).

1.                   X = ln(CA)

2.                   Y = ln(-rA)

 

 

X

 

0

 

-0.059

 

-0.115

 

-0.217

 

-0.311

 

-0.547

 

-0.899

 

Y

 

-8.85

 

-8.62

 

-8.74

 

-8.94

 

-9.13

 

-9.6

 

-10.30

 

A plot of Y versus X yields a straight line (Equation 1.25).

C                      Slope (α) = 2

C                      Intercept (I) = -8.5

C                      Reaction rate constant, k = exp(I) = 2.02 ´ 10-4 L/(mol·s).